PUMaC 2011 Team Sudoku Problem 9

Let w be the largest number such that w, 2 w and 3 w together contain every digit from 1 through 9 exactly once. Let x be the smallest integer with the property that its first 5 multiples contain the digit 9. A Leyland number is an integer of the form m^{n}+n^{m} for integers m, n>1. Let y be the fourth Leyland number. A Pillai prime is a prime number p for which there is an integer n>0 such that n!\equiv-1(\bmod~ p), but p \not \equiv 1(\bmod~ n). Let z be the fourth Pillai prime. Concatenate w, x, y and z in that order to obtain a permutation of 1, \cdots, 9. Write down this permutation.